Hardy’s inequalities for the twisted convolution with Laguerre functions

Abstract

Abstract In this article, two types of Hardy’s inequalities for the twisted convolution with Laguerre functions are studied. The proofs are mainly based on an estimate for the Heisenberg left-invariant vectors of the special Hermite functions deduced by the Heisenberg group approach.

Keywords

• Hardy’s inequality
• special Hermite expansions
• Laguerre function
• Heisenberg group
• Fourier transform